# Thread: Vector equations in R^3

1. ## Vector equations in R^3

Hi,

I'm trying to understand the question below:

The solution is:

Can someone explain how the parametric vector equation for 'z' was created? Also, how do you know what a "suitable restriction" is ?

- otownsend

2. ## Re: Vector equations in R^3

Originally Posted by otownsend

The solution is:
Here is such a line: $\ell(t)-\left\{ \begin{array}{l}-3t\\t\\3-6t\end{array} \right.$

Is it true that $A=\ell(-2)~\&~B=\ell(5)~?$

3. ## Re: Vector equations in R^3

The line must pass through the point (0, 0, 3) and have direction vector (-1, 3, -6). Then x= 0+ (-1)t= -t, y= 0+ 3t= 3t, and z= 3+ (-6)t= 3- 6t work.

In general, the line passing through $(x_0, y_0, z_0)$ with direction vector (A, B, C) has parametric equations $x= x_0+ At$, $y= y_0+ Bt$, and \$z= z_0+ Ct.